Blog

5000+ Members

MEETUPS

LEARN, CONNECT, SHARE

JOB POSTINGS

INDEED POSTINGS

Browse through the latest deep learning, ai, machine learning postings from Indeed for the GTA.

CONTACT

CONNECT WITH US

Are you looking to sponsor space, be a speaker, or volunteer, feel free to give us a shout.

[D] How to compute the “true” posterior for a generative model?

I have seen a few papers that show plots of the “true posterior” for a generative model on a toy problem.

Before I did not understand how this could be computed, but now maybe I am closer. I’m sure you can help me

Is this the way to do it? (See below)

Definitions and setup:

The generative model is p(x|z)*p(z). The posterior is p(z|x).

A particular x is given and we want to know the distribution p(z|x) for that x,

using p(z|x) ~ p(x|z)*p(x) ,

i.e. without evaluate the Bayes denominator.

1. Sample z from p(z),
2. evaluate p(x|z) for the given x, and multiply this by p(z) for the z that was sampled in step 1. This gives an “unnormalized” probability for this particular z.
3. Accept this new z as a sample using MCMC, e.g. metropolis-hasting.
4. Repeat 1-3, and then eventually make a kernel density plot of the resulting z sample locations.